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# Math Question

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Let $$r$$ be the positive real solution to $$x^3 + \frac{2}{5} x - 1 = 0.$$ Find the exact numerical value of $$r^2 + 2r^5 + 3r^8 + 4r^{11} + \dotsb.$$

Thank You!

Jan 5, 2020
edited by NewMember  Jan 5, 2020

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From the formula for a geometric series, the sum is 19/3.

Jan 5, 2020
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Let $$r$$ be the positive real solution to $$x^3 + \dfrac{2}{5} x - 1 = 0$$.
Find the exact numerical value of $$r^2 + 2r^5 + 3r^8 + 4r^{11} + \dotsb$$ .

Jan 6, 2020